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Question 30672
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Circular Motion: Advanced — Kepler from Circular Orbit MCQ

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Advanced — Kepler from Circular OrbitHardQuestion 30672

Question

Deriving Kepler's third law from circular orbit: if v = √(GM/r) and T = 2πr/v, then T ∝:
  1. A
    r^(1/2)
  2. B
    r^(3/2)
    Correct
  3. C
    r²
  4. D
    r^(2/3)

Correct answer

r^(3/2)

Explanation

T = 2πr/v = 2πr/√(GM/r) = 2πr×√(r/GM) = 2π√(r³/GM). So T ∝ r^(3/2), confirming Kepler's third law.

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